Lesson 6.2 Congruent Angles pp. 214-220

Objective: To identify, prove, and apply theorems relating to congruent angles.

EXAMPLE 1 Prove: All right angles are congruent.

Theorem 6.3 Supplements of congruent angles are congruent.

EXAMPLE 2 Prove: Theorem 6.3

EXAMPLE 3 Prove: If mAXB = mDXY, then mAXD = mBXY

Theorem 6.4 Complements of congruent angles are congruent. 1 2 3 4 exercise 8

Theorem 6.5 Angle congruence is an equivalence relation. Reflexive: A  A Symmetric: If A  B, then B  A. Transitive: If A  B and B  C, then A  C.

10. Transitive prop. of congruent ’s Given: A  B and B  C Prove: A  C

Statements Reasons 1. A  B B  C 1. Given 2. mA = mB mB = mC 2. Def. of  ’s 3. mA = mC 3. Trans. prop. of equality 4. A  C 4. Def. of  ’s

12. Symmetric prop. of cong. ’s Given: A  B Prove: B  A

Statements Reasons 1. A  B 1. Given 2. mA = mB 2. Def. of  ’s 3. mB = mA 3. Symm. prop. of equality 4. B  A 4. Def. of  ’s

13. Reflexive prop. of cong. ’s Given: mA = mA Prove: A  A

Statements Reasons 1. mA = mA 1. Reflex. prop. of equality 2. A  A 2. Def. of  ’s

Theorem 6.6 Adjacent Angle Sum Theorem. If two adjacent angles are congruent to another pair of adjacent angles, then the larger angles formed are congruent. exercise 15

Theorem 6.7 Adjacent Angle Portion Theorem. If two angles, one in each of two pairs of adjacent angles, are congruent, and the larger angles formed are also congruent, then the other angles are congruent. exercise 16

Theorem 6.8 Congruent Angle bisector Theorem. If two congruent angles are bisected, then the four resulting angles are congruent. exercise 17

Homework pp. 218-220

Reasons for 1-6, p. 218. 1. Given 2. Def. of cong. ’s 3. Vertical Angle Theorem 4. Def. of cong. ’s 5. Substitution 6. Def. of cong. ’s

■ Cumulative Review 21. All right angles are congruent. (Theorem 4.1) Diagram each theorem listed below. 21. All right angles are congruent. (Theorem 4.1)

■ Cumulative Review Diagram each theorem listed below. 22. If one angle of a linear pair is right, so is the other. (Theorem 4.3)

■ Cumulative Review Diagram each theorem listed below. 23. Adjacent supplementary angles form a linear pair. (Theorem 4.4)

■ Cumulative Review 24. Vertical Angle Theorem. (Theorem 4.5) Diagram each theorem listed below. 24. Vertical Angle Theorem. (Theorem 4.5)

■ Cumulative Review Diagram each theorem listed below. 25. Congruent supplementary angles are right angles. (Theorem 4.6)